It is widely believed that Morgana's betrayal was brought about by a combination of factors. Her fear of her gifts and of the reactions of her loved ones should they find out. Uther's continued persecution of those like her. The appearance of a sister who cared for her and who could teach her. Merlin's perceived betrayal.
In truth, none of these had any bearing on Morgana's decision to turn her back on those who loved her. Her choice was made during the course of one insignificant conversation.
Previously...
It was an ordinary day in Camelot.
"Merlin! Where's my dinner?"
Merlin winced. "Ahhh..." He knew he'd forgotten something.
"Well, don't just stand there, you buffoon! Go and get it!"
"Yes, sire."
Arthur watched in satisfaction as Merlin hurried out of the room (choosing to ignore the distinct lack of respect with which his manservant had used his title). Although he was considerably less pleased when Morgana waltzed into his chambers a few moments later, looking half-amused and half-disapproving.
"Really, Arthur. Must you be so hard on him? You know he does his best."
Arthur snorted in a rather unprincely fashion. "It's hardly my fault that his best is worse than any other servant in the kingdom."
Morgana rolled her eyes. "You're being ridiculous, Arthur. That boy would lay down his life for you – has done, in fact – though I personally cannot understand why. He may not be the most efficient servant but no one can deny his loyalty and courage."
"That is true," Arthur murmured, after a moment's contemplation. "But still, Morgana. I don't think you're fully aware of the depths of his ineptitude. I mean, the idiot once fed me rat, for goodness sake!"
Morgana's jaw dropped. "Rat?"
"Oh, yes," said Arthur, nodding grimly. "During the famine. After that, ah, incident with the unicorn."
"During the..." Morgana's eyes narrowed. "Hold on. You mean to tell me that when I came to you and asked you for your help, you and Merlin fed me RAT?"
And really, a discovery like that is enough to make anyone switch sides, isn't it?